Polini2016_Article_ConcurrentToleranceDesign---蔡溥雍.docx
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Res Eng Design (2016) 27:2336 DOI 10.1007/s00163-015-0203-2ORIGINAL PAPER Concurrent tolerance designWilma Polini1Received: 19 September 2014 / Revised: 5 August 2015 / Accepted: 3 September 2015 / Published online: 16 September 2015。 Springer-Verlag London 20151 3Abstract Technical drawings are constituted by three components that are strongly correlated: the geometry showing the part shape, the dimensions defining the part volume and the tolerances establishing the variability of the two previously described components. A general method- ology to assign the tolerances, especially geometric toler- ances, to all the components of an assembly has not been clearly defined up to now. This is probably due to the complexity of the problem and to the existing gap between the existing standards and the industrial designers com- mon practices. In this work, a new general methodology to assign dimensional and geometric tolerances to all the components of an assembly with a concurrent design approach is proposed. It takes into consideration the rela- tionships between tolerances and a set of design principles that have been naturally extracted from the standards and literature and from a deep discussion with the Italian Association of Industrial Designers. In order to demon- strate and validate the proposed approach, the methodology has been applied to two real case studies: a volumetric gear pump and a pneumatic actuator.Keywords Geometric tolerance Tolerance assignment Concurrent design Tolerance design1 IntroductionGeometric dimensioning and tolerancing (GD&T) is the result of studies and teamwork among research institutions and firms in order to define a complete design language. In particular, it is a tool to specify the requirements related to the design and to the technical representation of a part, which takes into account functional and assembly princi- ples. GD&T consists of symbols, rules, definitions and conventions. Moreover, it is a mathematical language that may be used to specify the shape, the dimensions, the orientation and the position of part features. This language allows one to translate, in a logical and unequivocal way, the designers ideas by eliminating the ambiguities of the implicit representation inherent to the previous coordinate tolerancing system (Wilson 1996). GD&T improves the communication between product designer and manufac- turing planner, since it supplies the tools to unequivocally interpret the design specifications of a drawing and, then, to minimize the arbitrary assumptions of manufacturing. It leads to a better manufactured product, since the design, the manufacture and the verification occur through the same descriptive language. GD&T constitutes a technique that, if applied in the right way, guarantees an effective and relatively inexpensive manufacture of the designed parts. Therefore, GD&T is an international language that is used to precisely describe parts with technical drawings. Moreover, GD&T may allow the manufacture to increase the width of the geometric tolerance zone, due to either the exploitation of dimensional tolerance zone (called toler-& Wilma Polini poliniunicas.it1Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Via Gaetano di Biasio 43, 03043 Cassino, Italyance bonus) or the reduction in functional requirements in light of manufacturing considerations. In this way, it is possible to decrease the manufacturing costs.All these advantages of GD&T help tolerance assign- ment when the concurrent design of product, process and24Res Eng Design (2016) 27:2336manufacturing system occurs in an integrated way. Func- tional design of a product may need great effort in terms of time and cost, because it must take into account the set of choices concerning the product, the process, the manufac- turing and the inspection systems that are strongly related. A concurrent approach emphasizes the complexity of the design process because it imposes that all the choices mentioned above should be carried out at the same time. Functional, technological and economical requirements are simultaneously taken into consideration. Further elements that complicate the functional design are the large number of part components to treat.Any changes in manufacturing process or system and evolutions in the performances of an existing product may require the redesign of the whole product. Even a small upgrade of existing products may need a long time and many resources. Lastly, the rules of functional design are domain of the older designers at a company. They are often not formalized and have a heuristic nature. In fact, these rules are the results of experience. Therefore, young engineers engaged by a firm may not have enough time for training, or they may learn directly on the job in the absence of the design experts of the firm. This results in projects not satisfying the previously defined requirements. GD&T reduces design complexity and young designers work. Moreover, the development of computer-aided tools that use drawings, in a file format, to communicate among product design and manufacturing planning minimizes human interactions and consequently design time in an automated environment. These tools must necessarily use a standardized language; they are becoming strategically critical in order to better exploit the design resources where they are geographically placed: they may belong to dif- ferent firms or to different centres of the same firm that are placed all around the world.Tolerance design is a stage of product design. The research on tolerance design has defined an iterative method, starting from a first tolerance assignment and ending with the definition of optimal values (Zeid 1991). Once all tolerances have been assigned to the part features that are critical from a functional point of view (tolerance assignment), tolerance analysis is performed. This stage aims to evaluate how the combined effect of all the pre- viously established tolerances influences the assembly characteristics in order to verify that all the design requirements are met. Subsequently the interactions between the defined tolerances are analysed in order to verify that the parts work correctly together. Therefore, the critical functional requirements of the assembly are cal- culated as a function of the previously defined tolerances and are compared with the constraints due to assembly or use. Finally, feasible or economic aspects are considered on the basis of both available processes and costevaluations. If the results are not satisfactory, one must modify the previous tolerance assignment. The whole tol- erance design is usually defined as tolerance synthesis.This work focuses on the tolerance assignment in the detailed design, which is the third step of the design pro- cess. In the literature, very few works dealing with this task exist. This is due to the peculiar nature of this topic: it presents as many different problems as there are design projects. The solution of these problems is entrusted to the designers experience. Lanzotti et al. (2000) assign the dimensional and geometrical tolerances on the basis of a feature classification; they consider form and dimensional tolerances of internal or external features. The concept of relations between features is used to allow the extension of the product model from conceptual to detailed design stages in Bradley and Maropoulos (1998): feature relations are an integrated representation system for dimensioning, tolerancing and connectivity modelling. Ballu and Mathieu propose a model that allows one to express fully several points of view: functional, standards, inspection and man- ufacturing (Ballu and Mathieu 1995). A computer-aided tolerancing system is shown in Tsai and Wang (1999): it assists the designer, especially in evaluating the tolerance accumulation of an assembly. The method introduced in Clement et al. (1994), Salomons et al. (1996) and Weill (1997) generates tolerances from contact relations expres- sed as associations between surfaces (Technologically and Topologically Related Surfaces, TTRS). In Anselmetti (2001), geometric specification on key component is gen- erated by rules involving the types of features and a user- defined priority order among them. Hu and Xiong (2005a,b) identify constraints to the relative motion among parts that they use to define suitable geometric control on fea- tures. Mejbri et al. (2003, 2005) decompose a global geo- metric functional requirement of a mechanism into geometric specifications defined on key components. The tolerances are defined by the user as special geometric tolerances whose datums are all located on a single base part of the assembly. For each requirement, a chain of contacts is built from the toleranced part to the base part. This allows to transform the original, external datums into regular datums on the same part. More recently in Armil- lotta and Semeraro (2011), the methods available for the specification of geometric tolerances, from common engi- neering practice to the development of computer-aided support tools, are described and compared. In Panneer and Sivaramakrishnan (2012), an integrated methodology is suggested for value specification and for checking the coherence and completeness of position, symmetry and perpendicularity tolerances based on distribution of mini- mum allowance. In Saravanan et al. (2014), a nonlinear combinatorial optimization problem is framed based on assembly function requirement (AFR) in order to optimizeRes Eng Design (2016) 27:233625the tolerance values. In Lu et al. (2012), an optimization algorithm is proposed to achieve concurrent tolerance design with a game theoretic approach.All these approaches, shown in the literature, do not develop a framework, generally effective, supporting the reasoning about tolerance choices. Moreover, they are applied to assemblies constituted by few and simple-shape parts.This work shows a new general methodology to assign dimensional and geometric tolerances to all the components of an assembly with a concurrent design approach. It takes into consideration the relationships between tolerances and a set of design principles that have been naturally extracted from the standards and literature and from a deep discussion with the Italian Association of Industrial Designers (IAID). A collection of rules to assign tolerances on the basis of the pursued functionality is, therefore, defined. These rules enable also to choose the necessary datum reference frames and material modifiers. Those rules help designer during the detailed design, where classically the tolerance approach is defined. In order to demonstrate and validate the proposed approach, the methodology has been applied to two real case studies: a volumetric gear pump and a pneumatic actuator.The paper is organized as follows. Firstly, the proposed methodology to tolerance design is presented together with some details on design rules. Then the application of the proposed method to a volumetric gear pump and to a pneumatic actuator is described in order to prove its effi- cacy and efficiency.2 Design methodologyThe proposed methodology to assign tolerances is a critical step of the functional product tolerance design. The pro- posed method is a set of decisions for carrying out a first assignment of tolerances, as shown in Fig. 1. It involves eight sequential choices that pass from the product per- formance to a promising set of dimensional and geometric tolerances. It may be used for single parts or assemblies.The first choice concerns the definition of the nominal geometry and the mechanical resistance, in terms of con- stitutive material, of a product, by taking into account the applied stresses, such as static or dynamic loads and tem- perature gradients. The product shape is defined together with its preliminary dimensions as a function of the chosen material in order to guarantee that the resistance require- ments are met.From the second to the eighth choice, there is the assignment of the geometric tolerances on the basis of the newly proposed approach.The second choice involves the identification of all the technical functions that the product should perform, by analysing the product working.The third choice translates the functionality of the design assembly in all the couplings or kinematic con- straints among assembly components that are needed for the assembly to work correctly. Then, it defines the pairs of assembly components involved in each technical function. The following steps from the fourth to the eighth choice that reason on the need of dimensional and geometric controls are implemented for each pair of components belonging to each technical function. The features of each pair of components that are involved in each technicalfunction are identified and processed as follows.The fourth choice assigns the dimensional tolerances to each pair of features by evaluating whether the coupling should occur with an interference, with a clearance or in an uncertain way. The accuracy required by the design spec- ification is also considered. Many standardized kinds of couplings exist in the literature (Straneo and Consorti 1991): for each of them, dimensional tolerances are fixed. The following four choices (from fifth to eighth) provide the geometric tolerances to characterize the functional aspects of each couple of features. They reflect the sequence of geometric controls supplied by the different classes of geometric tolerances. The order of geometric controls is decreasing: this means that the tolerance class allowing the greatest control, i.e. location tolerance, is assigned first. Run-out and profile tolerances are assigned lastly, since they are scarcely used in practice, due to theirpeculiar nature.The fifth choice evaluates whether it is needed to locate the features of each pair of components. Therefore, the necessity of a location tolerance is checked and, in the case of an affirmative answer, the datum reference frame (D.R.F.), the need of the material modifier (M or L) on the D.R.F., the tolerance kind (position, concentricity, or symmetry) and the need to use the material modifier (M orL) or the projected tolerance zone (P) on the tolerance feature are completely defined. The term POSITION near the material modifiers means that they may be applied on the datum reference frame or on the tolerance feature only for position tolerances.The sixth choice evaluated whether it is needed to orient the features of each pair of components. This means that if angular control of a feature greater than that due to a previously assigned position tolerance is needed, an ori- entation tolerance should be specified too. At the same time, if no position tolerance has been previously assigned, this step allows control of the feature orientation. An ori- entation definition must provide a D.R.F., the need of the material modifier (M or L) on the D.R.F., the tolerance type (parallel, orthogonal or inclination) and the need to use the26Res Eng Design (2016) 27:2336Fig. 1 New methodologymaterial modifier (M or L) on the tolerance feature or to apply the tolerance to a tangent plane (T).The seventh choice specifies a form tolerance if a form specification greater than that due to position or orientation tolerances is needed. A form tolerance assignment involves the definition of tolerance type (straightness, flatness, roundness or cylindricity) and the maximum material modifier M that is typically used for straightness.The eighth choice specifies run-out or profile tolerances in peculiar applications. The assignment of a run-out or a profile tolerance involves the definition of a D.R.F., the need of the material modifier (M or L) on the D.R.F. and the definition of the tolerance type (circular or total run- out, line or surface profile).All the steps of the design methodology are reported in Table 1, whereas the steps 48 should be repeated for each couple of assembly features involved in each pair of assembly components, steps 38 should be repeated for each pair of assembly components involved in each tech- nical function, and steps 28 should be repeated for each technical function.This geometric characterization of each pair of compo- nents is carried out by means of design criteria. Design criteria are rules, whose if-conditions make reasoning on the working of the analysed pair of parts and whose actions assign geometric tolerances to the part features. Examples of design criteria are the assignment of flatness to planes that must guarantee an adhesion, or the attribution of a concentricity where a mass balance is required, or the definition of a projected tolerance zone where interferences among coupling parts must be avoided. Moreover, the choice of a datum reference frame may follow some simple and unequivocal rules, such as a datum should be easily accessible for verification and it should be manufactured with the accuracy required by the design specifications. Some details on these design criteria are described in the following paragraph.Once a geometric tolerance is assigned to a pair of assembly components, it is verified that this tolerance actually satisfies the functional requirements identified at the first and the second steps of the proposed method: this comparison is shown as feedbacks in the flow chartRes EngDesign (2016) 27:233627Table 1Design methodologyNumberDescriptionExplanation0Product dimensioningTo define the product shape together with its preliminary dimensions as a function of the chosen1 Products technical functions identificationFor each technical function2 Identification of the pairs of assembly componentsFor each pair of assembly components3 Identification of the couples of assembly featuresFor each couple of assembly featuresmaterial in order to guarantee that the resistance requirements are metTo identify all the technical functions that the product should perform by analysing product workingTo identify the pairs of assembly components involved in each technical function that means whose assembly allows the product to explicate that functionTo identify all the couples of features involved in assembly4 Dimensional tolerance assignment To assign the dimensional tolerances by evaluating whether the coupling should occur with aninterference, with a clearance or in an uncertain way5 Location tolerance assignmentTo check the necessity of a location tolerance. If yes, to define datum reference frame (D.R.F.),material modifier (M or L) on the D.R.F., tolerance kind (position, concentricity, or symmetry) and material modifier (M or L) or projected tolerance zone (P)6 Orientation tolerance assignmentTo evaluate whether it is needed to orient the features. This means that if an angular control of afeature greater than that due to a previously assigned location tolerance is needed, an orientation tolerance should be specified too. If no location tolerance has been previously assigned, this step controls orientationIf yes, to define datum reference frame (D.R.F.), material modifier (M or L) on the D.R.F., tolerance kind (parallel, orthogonal, or inclination) and material modifier (M or L) or tangent plane (T)7 Form tolerance assignmentTo evaluate whether it is need to assign a form specification. This means that if a form controlgreater than that due to position or orientation tolerances is needed, a form tolerance should be specified tooIf yes, to define tolerance type (straightness, flatness, roundness or cylindricity) and material modifier M for straightness8 Profile or run-out tolerance assignmentTo evaluate whether it is needed to assign run-out or profile tolerancesIf yes, to define datum reference frame (D.R.F.), material modifier (M or L) on D.R.F. and tolerance type (circular or total run-out, line or surface profile)shown in Fig. 1. If the functional requirements are not satisfied, refine the technical functions and reiterate the proposed methodology. Otherwise, the following step of the tolerance design process may be carried out, i.e. the tolerance analysis. Tolerance analysis aims to determine the variability of a design function that depends on the assembly, when the previously fixed tolerances are var- ied. If all the tolerances assigned to the assembly com- ponents do not satisfy the design constraints, adjust the design by remaking the tolerance assignment. Otherwise, it is possible to carry out the last step of the design process. This stage takes into account the manufacturing or economic constraints related to the tolerances previ- ously assigned on the basis of functional reasoning. Reiterate the design process if the constraints are not satisfied. At the end of this process, a set of dimensional and geometrical tolerances, optimal in terms of func- tionality, manufacturing and cheapness, are obtained.3 Design criteriaDesign criteria put functional requirements in touch with dimensional or geometric tolerances. The great difficulty in defining design criteria is that there are so many different problems in mechanical design that it may not make any sense to define general rules. At the same time, having a set of criteria may help young designers to approach the design process. This is fundamental, especially for geometric tolerances whose standards are often not well known and whose application may be very hard due to the unknown relationships between tolerances and functional perfor- mances. Therefore, the design criteria are a collection of rules that establish the tolerances to assign on the basis of the pursued functionality. Moreover, this set of rules includes some principles to choose both the datum refer- ence frame and the material modifiers. These design cri- teria have been defined by collecting information of the28Res Eng Design (2016) 27:2336literature (Meadows 1995; Clement et al. 1994; Cross et al. 1996; Creveling 1996) and by discussion with the Italian Association of Industrial Designers (IAID). The design rules collected up to now are many, but they need to be further widened and updated in time by discussing con- tinuously with mechanical designers.As concerns the dimensional tolerances, the assignment is simplified by the existence of tables where the application fields of the most common couplings, basic hole or basic shaft, are shown (Lee and Woo 1990). Analysing these tables, it is possible to note that the shafts are generally characterized by tolerances more narrow than those pro- vided for holes. This is due to the fact that shafts are inexpensive, but have low tolerances compared to holes. Actually, the basic hole is preferred by precision industry, such as automotive, aeronautic manufacture, machine tool, internal combustion engines and pumps. This is due to the fact that a hole inspection is generally carried out by gauges that are more easier to manufacture than fork gauges used for shaft. The basic shaft is used where the least accuracy is required, such as agricultural or textile machines.As concerns the form tolerances, a flatness control is generally used to provide a flat surface for a gasket or seal, to attach a mating part or to make better contact with a datum plane. Moreover, straightness control is preferred if associated with a maximum material condition (MMC), when it is needed to guarantee a right functional relation- ship between parts to couple, such as a pin or a shaft and a hole. Finally, a common reason for using a circularity or cylindricity control on a drawing is to limit the out of round of a shaft diameter. In certain cases, lobbing of a shaft diameter will cause bearings or bushings to fail prema- turely. The value of the form tolerance range may be decided with the help of a rule-of-thumb that is based upon the norms of production and probabilities: a design form tolerance requirement on a stable rigid part should be equal to, or less than, one-half of the overall size tolerance for justification as a specified form tolerance.Orientation tolerances control the angular position of a plane surface or of a feature of size (FOS). An interesting application of orientation tolerances is with the tangent plane modifier. The tangent plane modifier denotes that only the tangent plane established by the high points of the controlled surfaces must be within the parallelism tolerance zone. When the tangent plane modifier is used in orienta- tion call-outs, the orientation of the toleranced surfaces is not controlled. This specification may be usefully applied to mating planes, since it is less strong than the orientation tolerance applied to the whole surface.A position tolerance defines the location of a FOS from its true position. When specified on regardless of feature size (RFS) basis, a position tolerance control defines a tolerance zone that the centre, axis or centre plane of theFOS must be within. When specified on an MMC or least material condition (LMC) basis, a position tolerance con- trol defines a boundary, often referred to as the virtual condition that may not be violated by the surface or sur- faces of the considered feature. In comparison with coor- dinate tolerancing, a tolerance of position offers many advantages, such as it provides larger tolerance zones by using cylindrical tolerance zones in spite of squared ones and it permits additional tolerances taken by dimensional one and datum shift. Moreover, it prevents tolerance accumulation, since the position errors of each FOS are defined with respect to the datums; it permits the use of functional gauges that simplify the part inspection. All these reasons contribute to a clear interpretation and a decrease in manufacturing lubricants costs. Position toler- ance is commonly used to control four types of part rela- tionships: the distance between features of size, such as holes, bosses, slots and tabs, the location of features of size or patterns of features of size, the coaxiality between fea- tures of size and the symmetrical relationship between features of size. When designing products with fasteners, fixed and floating fastener schemes are a convenient design tool. A fixed fastener assembly is one where the fastener is held in place by one of the components of the assembly. This means that the holes in one component of the assembly are clearance holes, while the hole in the other component is threaded or a press fit, like a dowel pin. The floating fastener assembly is where two (or more) com- ponents are held together with fasteners (such as bolts and nuts), and both components have clearance holes for the fasteners.When specifying a position control, the designer must specify under which material condition the control is to apply. The MMC symbol is advantageous when mating is most important. The least material concept is usually used for features when the preservation of material is of great importance and cost is a significant factor. It is used when wall thickness is thought to be endangered and the holes stand a chance of approaching a breakout condition. It is also used on casting drawings to assure that in subsequent machining operations, enough material is available to allow a machine cut to clean up the part surface. The RFS concept preserves balance better than either the MMC or LMC symbol concepts, protects mating as well as the MMC symbol concept (but not as well as the LMC con- cept) and creates tighter, more restrictive tolerances on the average produced part. This runs the risk of increasing the cost of the overall product and should be used only when it is determined that the use of the MMC or LMC concepts may endanger part function. Further design principles are related to the use of a projected tolerance zone or a zero tolerance at MMC. A projected tolerance zone modifier should be specified in bolted joint applications, wheneverRes Eng Design (2016) 27:233629the height of the clearance hole is greater than the depth of the threaded hole. A zero tolerance at MMC should be considered whenever the function of a FOS is assembly. Many further design criteria are related to the datum ref- erence frame, to coaxial features and to noncylindrical features (Creveling 1996).The design criteria are summarized in Table 2.4 Application examples4.1 Gear pumpThe newly proposed methodology to tolerance assignment has been applied to the volumetric gear pump shown in Fig. 2. It is commonly used to draw up different types ofTable 2 Design criteriaAssignment ruleScopeAuthorityTo provide a flat surface for a gasket or sealFlatness toleranceFoster (1994)To attach a mating partFlatness toleranceFoster (1994)To make better contact with a datum planeFlatness toleranceFoster (1994)Applied to a FOS with a MMC to guarantee a right functional relationship between parts to couple, such as a pin or a shaft and a holeTo limit the lobes (mass balance) that will cause bearings or bushings to fail prematurelyForm tolerance range on a stable rigid part should be equal to, or less than, one-half of the overall size toleranceStraightness toleranceFoster (1994)Circularity or cylindricityFoster (1994)Form tolerance rangeFoster (1994)To control mating planes, since it is less strong than the same tolerance applied to the whole surfaceOrientation tolerance and tangent plane modifierAIPIA datum should be easily accessible for verificationDatumAIPIA datum should be manufactured with the accuracy required by the design specificationDatumAIPISpecify all the needed datumDatumAIPIPrefer to choice as datum the mating features of the two coupling partsDatumAIPITo control the distance between FOS, such as holes, bosses, slots and tabsPosition toleranceKrulikowski (1998)To control the location of FOS or pattern of FOSPosition toleranceKrulikowski (1998)To control the coaxiality between FOSPosition toleranceKrulikowski (1998)To control the symmetrical relationship between FOSPosition toleranceKrulikowski (1998)It is helpful when mating is most importantMaximum material conditionFoster (1994)It is usually used for features when the preservation of material is of great importance and the cost is a significant factorIt is used when wall thickness is thought to be endangered and the holes stand a chance of approaching a breakout conditionIt is also used on casting to assure that in subsequent machining operations, enough material is available to allow a machine cut to clean up the part surfaceLeast material conditionFoster (1994)Least material conditionFoster (1994)Least material conditionFoster (1994)It preserves mass balance for rotating partsRegardless of feature sizeFoster (1994)It protects mating as well as MMCRegardless of feature sizeFoster (1994)It creates tighter, more restrictive tolerances, and, therefore, it increases the product costTo avoid interferences among coupling parts (for example: in bolted joint when the height of the clearance hole is greater than the depth of the threaded hole)To assemble a mechanism, it is enough that the surfaces, resulting from virtual boundary conditions, are coupledRegardless of feature sizeFoster (1994)Projected tolerance zoneMeadows (1995)Assembling principleMeadows (1995)30Res Eng Design (2016) 27:2336Fig. 2 Gear pump Courtesy (Straneo and Consorti 1991)oil, fuel or lubricants. As known, it is constituted of a case(6) inside which a pair of toothed gears is housed: a pinion that takes the motion by a shaft connected with an engine (9), and a gear wheel (8) that is driven by the pinion. The case is joined to suction and outlet tubes on the two sides of the gears. Fluid is trapped laterally inside the hollow space between two consecutive teeth and the case, and it is car- ried from suction to outlet by the rotation of the gears. At the same time, the fluid does not come back to the suction side because of the seal between the two engaged teeth of the gears. A fixed clearance among case and gears is not able to preserve the lateral clearance of the gears, thus reducing the volumetric efficiency. Two mobile supports(7) that are moved near to the gear sides guarantee a minimum lateral clearance. A front cover (1) and an end one (4) complete the components of the designed pump. In this case, the newly proposed methodology has been used to define the required dimensional and geometric toler- ances that have been compared with those of the literature (Straneo and Consorti 1991). Once the nominal pumpgeometry has been defined, four technical functions that thecover. A perpendicularity tolerance is assigned to the internal surface of the cover related to the axis of the hole with 18.5 mm diameter (see Fig. 3). This orien- tation control implies indirectly a flatness control useful for the third technical function. Moreover, it is necessary to add the parallelism of the internal surface and the external one, to correctly transfer the motion from outside. As concerns with the two supports, the coaxiality of the 20-mm holes with the 18.2-mm holes (see Fig. 4) must be guaranteed, in order to assemble and to make the pump working correctly. Therefore, the roundness and the parallelism of the old design (Fig. 4 on the left) have been replaced by the coaxiality of the two holes coupling with the shaft of gear wheel, as shown in Fig. 4 in the right. These changes have been approved by designers of IAID too.A further perpendicularity tolerance is also needed among the hole mounting the pinion axis and the plane surface in contact with the internal surface of the front cover, in order to avoid obliqueness between the axis of the pinion with respect to the surface mating with the front cover. To transmit the movement between the two toothed gears, a parallelism control between the axes of the two hole coupled with the gears is necessary. The toothed gears require a circular run-out on the tooth surface in order to guarantee mass balance and minimize the eccentricity during the movement of the two gears (see at the top of Figs. 5, 6). The case needs a parallel tolerance among the surfaces mated with the front and the end covers in order to guarantee the assembly and the correct working of the pump (see at the bottom of Fig. 7). Moreover, a perpendicularity tolerance assigned to the surface mated with the internal surface of the front cover assures a correct power drive. The second technical function involves the front coverand the two mobile supports. Two bushings are provided between the shafts and the supports. The dimensional tolerances are fixed for each coupling on the basis of tables found in the literature: the hole on the supports has a dimensional tolerance of?018.2?0.05 mm (see Fig. 4), while the gear shaft has apump must perform have been identified. The first is the power drive between two parallel gears, the second is guiding of the two rotating shafts holding pinion and gear wheel, the third is the seal at the entrance shaft connected with the engine, and the fourth is the axial compensation ofthe clearances.dimensional tolerance of 18-0.01 mm (see Figs. 5, 6).-0.02No further geometric specification is needed to guar- antee this guide function. The third technical function, i.e. the seal at the entranceshaft connected with the engine, involves the front cover whose hole has a dimensional tolerance of?0.0218.5?0mm and couples with the shaft of the driving-0.01 The first technical function involves many componentswheel that has a dimensional tolerance of 18-0.02 mmof the pump: the front cover, the supports, the pinion,the wheel gear and the case. In order to transmit the correct motion, it is convenient to avoid the rotation axis of the pinion being oblique with respect to the front(see Figs. 3, 5). Finally, the fourth technical function, i.e. the axial compensation of the clearances, involves the two supports. The plane surfaces of the supports go intoRes Eng Design (2016) 27:233631Fig. 3 Tolerance assignment to the front cover Courtesy (Straneo and Consorti 1991) 25-0,010,01 D21B0,01 A0,03 BCDA0,02 A(a)18,2+ 0,050+ 0,0220+ 0,010,01(b)00,03CFig. 4 Tolerance assignment to the support: a old design Courtesy (Straneo and Consorti 1991); b new design-0.01contact with the flanks of the wheels, with one of the internal sides of the covers and with internal side of the pump casing. Therefore, a dimensional tolerance is applied to the depth of each support equal to 250mm. Moreover, a parallelism tolerance of 0.02 mm is applied as regards the datum A on the surface of the support that goes into contact with the flank of the wheel (see Fig. 4). Finally, it is needed to consider that it is applied a totalrun-out tolerance that substitutes the circular run-out and the straightness tolerances of the previous design, to take into account the run-out of the flanks of the wheels during their revolution. The total run-out should be assigned to the flanks of the toothed wheels, but generally the flanks are machined by grinding; this manufacturing process limits the run-out deviations. The coupling between support and pump casing involves a dimensional32Res Eng Design (2016) 27:2336Fig. 5 Tolerance assignment to gear wheel Courtesy (Straneo and Consorti 1991)Fig. 6 Tolerance assignment to pinion shafts Courtesy (Straneo and Consorti 1991)tolerance H6-e5, a circular tolerance of 0.015 mm for the support (see Fig. 4) and of 0.01 mm for the pump (see Fig. 7) in order to guarantee the contact between the coupled surfaces. Finally, a flatness tolerance of0.08 mm is applied to the side of the back cover (see Fig. 8).4.2 Pneumatic actuatorThe second example is a pneumatic actuator with twelve pistons that are actuated by pneumatic valves. It is a part of a machine to manufacture wood.The original design is shown in Fig. 9. Proceeding as made for the gear pump, the func- tional requirements of the part are identified. In particular, the pistons, once coupled with further elements, have to press an abrasive paste on a plane surface to machine. To do this, a guide for the pistons that involves a coupling H7-g6 between the pistons axis and the guide was designed (see Fig. 10). The guide has an O-ring in poly-tetra- fluorine-ethylene (PTFE) charged by carbon fibres with a slide to reduce the friction. There is a gasket of polyurethane to avoid the compressed air going out of the down side of the part, whereas the pistons are seated. To limit the deviation of the pistons axis during its movement, a perpendicularity tolerance of0.05 mm that originally was applied as regard to datum C has been applied. The second requirement is to rightly assemble the part thatmeans to define clearly the location of the 24 threaded holed M5, of the pistons, of the rods, of the four threaded holes M6 on the side surfaces of the part. The new design put location tolerances on the axes of the holes and pistonsRes Eng Design (2016) 27:233633Fig. 7 Tolerance assignment to pump case Courtesy (Straneo and Consorti 1991)Fig. 8 Tolerance assignment to end cover Courtesy (Straneo and Consorti 1991)(see Fig. 10), whereas the original design used dimen- sional tolerances. The rods and the four holes M6 remain unchanged, since they do not constitute a pattern and they have different values of tolerances.The new procedure has introduced a new datum reference system of the part that is constituted bydatum D (i.e. the bottom surface of the part that is called A in the original design) that is constrained to datum A (the up surface of the part) by a parallelism tolerance, see Fig. 10. In this way, the surface to use for locating the part during manufacturing and inspec- tion was clearly defined.0,02CN 12+ 12 fori M5 05+ 0,2 341 30,05C275,6 0,03048,5+ 0,0528,8 214+ 0,1041+ 0,10010+ 0,1CH= 1718 h7 E44,5 0,0255,5 0,02533+ 0,050216 H8M20X1 1,5 191014 H99+ 0,05+ 0,0500 11,3 0,0334,3 0,0357,3 0,0380,3 0,03103,3 0,03126,3 0,03149,3 0,03172,3 0,03195,3 0,03218,3 0,03241,3 0,03264,3 0,03Sez. A-A10+ 0,50A0,05 AN 2+ 2 fori M6 Gola UNI4386-E 0,4x0,2 1,7Particolare E 0,8 0,0510 g6 0,65 0,056 0,057 g68,9 0,050,5 0,03X300,5 0,03X45 = = C22N 12+ 12 fori M3 filetto utile 7,5 mmB1,550 0,343,5 0,3 10 corsa: 9,5 0,2 42 0,2 43,5 0,310 0,037 0,2 60 0,3Res Eng Design (2016) 27:23363,825 0,02512 0,2Fig. 9 Original design of pneumatic actuatorRes Eng Design (2016) 27:233635Fig. 10 New design of pneumatic actuator1 3To control the position, the new procedure introduces a perpendicularity tolerance of 0.02 mm and a paral- lelism tolerance of 0.05 mm. The first tolerance is applied to the longitudinal plane of the part that is used to locate the pistons. The second is applied to the axes of the threaded holes and of the pistons. In this way, it is assured the right alignment of the parts.5 ConclusionsThe analysis of the application examples underlines some important considerations strictly connected with the pro- posed methodology of tolerance assignment. A careful examination of the technical functions that must be imple- mented and the knowledge of the relationships between geometric tolerances allow us to correctly define the geo- metric controls that are effective for the designed device and to avoid a useless overlapping of tolerances that imply an increase in the manufacturing and inspection costs.Examples are the modifications of the design of the pump
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